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Malaysian Journal of Civil Engineering 25(2):254-266(2013)
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means
without the written permission of Faculty of Civil Engineering, Universiti Teknologi Malaysia
LOAD-MOMENT INTERACTION DIAGRAMS OF SLENDER PARTIALLY
ENCASED COMPOSITE COLUMNS
Saima Ali1*
& Mahbuba Begum2
1 Department of Civil Engineering, Ahsanullah University of Science & Technology, Dhaka-1208,
Bangladesh. 2Department of Civil Engineering, Bangladesh University of Engineering & Technology
*Corresponding Author: saima.ce@aust.edu
Abstract: Partially Encased Composite (PEC) Columns consist of thin-walled built-up H-shaped
steel sections with links welded near the flange tips and concrete cast between the flanges. To
predict the strength and ductility of slender PEC columns, Newmark’s numerical iterative
procedure is implemented. Overall column slenderness ratio, flange plate slenderness ratio and
concrete strength are the selected parameters to observe the variation of strength and ductility of
slender PEC column. Bending of column about both the strong and weak axis is considered to
observe the significance of the selected parameters. In strong axis bending, a decrease in strength
is found with the increase of overall slenderness ratio and flange plate slenderness ratio. Again,
failure envelope of column strength curve becomes smaller with the increase of overall
slenderness ratio. It implies the ductility of slender PEC column decreases with the increase of
the overall slenderness ratio. Moreover, similar behaviour is observed with the increase of flange
plate slenderness ratio. As the strength of concrete increases, strength of slender PEC column is
observed to increase by significant amount. Similar behaviour is observed in weak axis bending
along with some drop in strength.
Keywords: Strength, ductility, composite, slender columns, failure envelope
1.0 Introduction
Partially encased composite (PEC) column is an innovative steel concrete composite
column. Again, a steel concrete composite column is a combination of steel and
concrete accompanied with or without rebar. It is a compression member, comprising
either a concrete encased hot-rolled steel section or a concrete filled tubular section of
hot-rolled steel and is generally used as a load-bearing member in a composite framed
structure. In composite structure, the existing loading is resisted by both steel and
structural concrete. In PEC column, all the elements of the composite section are
completely encased by concrete except the flange portion of the hot rolled steel section.
Figure 1 and 2 illustrates the cross-section and elevation of a typical PEC column
respectively.
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 255
This innovative column consists of thin walled built-up steel section and concrete infill
is casted between the flanges. To resist local buckling between the flanges, transverse
links are provided at constant intervals. PEC columns are more commonly accepted than
other steel concrete composite columns as it minimizes the use of higher cost steel.
Besides, it enhances the economic compressive load capacity of concrete. The use of
this innovative system facilitates simple installation and removal techniques of the
formwork from concrete and also standard connections to the steel flange. Consequently,
it improves the speed of erection of steel structures.
Figure 1: Cross-section of PEC column
256 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
Figure 2: Elevation of PEC column
1.1 Background
Extensive experimental research is conducted on thin walled short PEC columns with
built up section by several research groups. Among these the work carried out by Fillion
(1998), Tremblay et al. (1998), Chicoine et al. (2000, 2003), Bouchereau and Toupin
(2003), Prikett and Driver (2006) is remarkable. A large number of tests were performed
on short PEC columns constructed with normal strength concrete subjected to eccentric
and axial loads, including static and cyclic conditions. Moreover, short PEC columns
with high performance concrete were also tested under pure axial compression as well
as combined axial and flexural compression.
Numerical investigations on short PEC column were done by Maranda (1999), Chicoine
et al. (2002) and Begum et al. (2007). All the researchers conducted finite element
analysis to study the behaviour of PEC column. Recently, Deng (2008) conducted
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 257
research on a half size two storey one bay steel plate shear wall specimen, with PEC
columns as the boundary elements. In addition, Dastfan (2011) did two large scale tests
on steel plate shear walls with built up PEC columns.
However, limited research works are performed on slender PEC column to predict the
strength of this innovative structure. Three long PEC columns were tested by Chicoine
et al. (2000) to study the overall buckling behaviour of these columns under monotonic
loading. Besides, Begum et al. (2007) conducted a finite element analysis on slender
PEC columns. Three 9.0m long PEC columns with a cross-section of 450mm × 450mm
× 9.75mm tested by Chicoine et al. (2000) were selected for finite element simulation to
predict the global buckling behaviour of slender PEC column. The slender PEC columns
were observed to fail by global buckling as well as local flange buckling.
The research on PEC columns with thin walled sections reveals that the behaviour of
short PEC column with normal and high performance materials are become relatively
well understood from the full scale extensive experimental and numerical investigations.
Design guidelines and axial capacity of short PEC column are well established and
included in Canadian steel design code (CSA-S16.09). However, design guidelines for
slender PEC columns are not included in the design code due to scarcity of ample
research on long PEC columns. Moreover, it is not possible to obtain a complete
understanding of various components from experimental investigations only due to high
cost and time requirement for full scale testing. No numerical study is yet performed to
predict the strength and ductility of slender PEC columns. In this regard, through a
numerical analysis, an attempt is made to represent the axial load and moment capacity
of slender PEC columns and also to observe the influences of several key parameters
which could not be studied by the experimental programs.
1.2 Objectives
The main objective of this study is to investigate the strength and ductility of slender
PEC column. To this end, column strength curve (interaction diagram) of slender PEC
column is formulated. Again, to develop the column strength curve of such an
innovative system, load to maximum moment curve is constructed of slender PEC
column. To formulate the load to maximum moment curve, Newmark’s numerical
iterative procedure is implemented. The slender column is assumed to bend under single
symmetric curvature bending about strong axis and also in weak axis in two parts of this
study. Finally, some potential variables that can influence significantly are considered to
observe their effects through observing the column strength curve of slender PEC
column.
258 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
2.0 Methodology
A slender column especially when it is loaded eccentrically has a significant reduction
in its axial load capacity due to moments resulting from lateral deflections of the
column. How the axial load capacity is affected by the lateral deflection, is illustrated in
Fig. 3 which shows a pin-ended column and subjected to eccentric loads. The moments
at the ends of the columns are
(1)
When the load P is applied, the column deflects laterally by an amount Δ, as shown in
Fig. 3. For equilibrium, the internal moment at the mid-height must be,
(2)
Figure 3: Forces in a deflected column
The ultimate axial load capacity of a slender column is determined using the cross-
sectional column strength curve (load-moment interaction diagram) as well as the load
PeM
)ΔP(eM
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 259
to maximum moment (P-M) curve of slender column. The former one is developed
using a procedure commonly adopted for reinforced concrete columns. The load to
moment curve for slender PEC column is plotted using the mid height deflections
calculated for each load level. The slender column P-M curve is then superimposed on
the cross-sectional interaction diagram. The point of intersection is the ultimate capacity
of the column (Wight and MacGregor, 2009).
The interaction diagram for short column is formulated as followed by Bouchereau and
Toupin (2002) and Prickett and Driver (2006). Bouchereau and Toupin (2002) and
Prickett and Driver (2006) predicted the capacity of eccentrically loaded columns from
load-moment interaction diagrams constructed using a procedure commonly adopted for
reinforced concrete columns. A linear strain distribution along the cross-section, based
on observations from the strain measurements taken during the test, is implemented for
the construction of this diagram. The extreme compressive strain is set at 3500με,
whereas the extreme tensile strain is varied from 0 to 10 times the yield strain of the
steel. For each strain gradient, the ultimate load and moment capacities are calculated
from the material and geometric properties of the composite cross-section. The
compressive force in the concrete, Cc, is calculated using the following expression,
assuming a rectangular stress block,
cβc
bcu
fαc
C 11 (3)
where,
bc= Net width of concrete block (i.e. excluding the web thickness of strong axis bending
and excluding the flanges for weak axis bending)
c = Distance between the extreme compression fibre and neutral axis
0.67cu
0.0015f0.85α 1 (4)
0.67cu
0.0025f0.97 1 (5)
To calculate the contribution of the steel to the capacity of the composite column, the
section is discretised in such a way as to have effectively uniform strain in each
individual piece. For strong axis bending, the flanges are considered to be one piece,
whereas the web is divided into ten pieces. On the other hand, for weak axis bending,
the web is considered as one piece and each flange is discretised into ten pieces.
(Prickett and Driver, 2006). The resultant force for each individual piece is calculated by
multiplying the area of the piece by its average strain. However, if the strain in the
individual piece exceeded the yield strain, the force resultant is determined by
260 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
multiplying the area of that piece by the yield stress. In calculating the area of a flange
piece in compression, the effective width, be is used by (Prickett and Driver, 2006).
Finally, the total load capacity of the composite column is determined by adding the
force resultants for concrete and steel and the moment capacity are obtained from the
summation of each force multiplied by its distance from the centerline of the column
cross-section.
To determine the second order deflection of slender PEC column at its mid-height,
Newmark’s (Newmark, 1943) non-linear numerical procedure is used. The steps
followed can be summarized as,
a) The length of the slender column is subdivided into several differential segments.
A unit deflection is assumed at the mid-height of the slender column and zero at
the ends. The deflection at other stations along the length is determined through
linear interpolation.
b) The total moment at each station along the length of the column is evaluated
using Eq. (2) for the selected level of axial load.
c) Using the moments obtained from the previous step the curvature at the selected
stations along the length of the column is computed.
d) Using the conjugate beam method the deflection at each station is calculated. This
deflection is compared to the assumed deflection.
e) If the computed deflections and the initial deflections are within prescribed limits
of 0.05%, an equilibrium solution is obtained. If not, the computed deflections are
substituted for the assumed deflections and the process is repeated until the
deflections converge.
The interaction diagram or column strength curve of the slender PEC column is
constructed using the cross-section interaction diagram and the P-M curves for the
slender PEC column at various levels of e/d ratios as shown in Fig. 4.
Figure 4: Formation of interaction diagram of slender PEC column
A2
D2
C2
B2
M=P.e2
P-M curve of slender PEC
column
M=P.e1
Axial Load
B1
C1
Column strength
Moment
Cross-section
strength
O
A1
D1
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 261
For different e/d ratios ranging from 0.05 to 50, the P-M curves are constructed using
the procedure described above. The selected e/d ratios are 0.05, 0.1, 0.2, 0.3, 0.4, 0.5,
0.6, 0.7, 0.8, 0.9, 1.0, 2.5, 5.0 and 50. When e/d ratio is 50, the amount of axial load is
nearly zero. These curves are superimposed on the cross-section strength curve of the
column. The M=P.e diagrams are also plotted for the different values of e/d ratios. Now,
horizontal lines (B1C1 and B2C2) is drawn from the intersection points (B1 and C1
respectively) of the cross-section interaction curve and the nonlinear P-M curve (curve
OD1 and OD2) for each eccentricity (e1 and e2 are shown). The point of intersection (C1)
of the horizontal line (B1C1) and line OA1 (M=Pe1) represents the axial load and
moment at the end of the column at failure. Similarly, point C2 represents the end
moment at failure at eccentricity e2. This process is repeated for the selected PEC
column (L/d=25) for the selected values of e/d ratios and the corresponding failure
points are determined. The slender column interaction curve (as shown by dashed line in
Fig. 4) is then drawn by connecting the failure points (Wight and MacGregor, 2009).
This curve shows the loads and maximum end moments causing failure of the given
slender column.
3.0 Parametric Study
3.1 Effect of overall column slenderness ratio (L/d) on column strength
The effects of overall slenderness ratio on the load-moment curve of PEC column are
shown in Fig. 5. In order to study the variation of strength, PEC columns of overall
slenderness ratio 5, 15, 20, 25 and 30 are selected. Since, slenderness might have a
significant effect on column strength, so small increments are considered to observe the
effect rigorously.
(a) Strong Axis Bending
Figure 5: Effect of overall column slenderness ratio (L/d) on interaction diagram of slender PEC
column (a) Strong axis
0
2000
4000
6000
8000
10000
0 200 400 600 800 1000
L/d = 5 L/d = 15 L/d = 20 L/d = 25 L/d = 30Moment (kN-m)
Ax
ial
Lo
ad
262 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
Figure 5(cont’): Effect of overall column slenderness ratio (L/d) on interaction diagram of
slender PEC column (b) Weak axis
From the interaction diagrams, it can be clearly seen that the area of the failure envelope
reduces significantly with the increase of the overall slenderness ratio of PEC column.
As the column gets slender, strength as well as ductility of the column reduces. Drop in
strength is more significant in weak axis bending compared to that on strong axis
bending. With the increase of the overall column slenderness ratio, more brittle
behaviour is clearly observed when weak axis bending is considered as the tension zone
of column strength becomes smaller. Considerable reduction in strength is found in
compression zone as compared to the same in tension zone of the five interaction
diagrams. From a short column (L/d = 5) to a slender column (L/d = 30), an average
reduction of 7% is noted. However, as the column slenderness ratio increases from 15 to
20, only 3% average drop in strength is found. On the other hand, as mentioned above, a
significant drop in strength is found when slenderness ratio is varied from 20 to 25. An
average reduction rate of 8% is found in such condition. Finally, strength of slender PEC
column decreases with an average value of 9% as the slenderness of column is turned
from 25 to 30. Under weak axis bending, on average 3% greater drop in column strength
is observed.
3.2 Effect of flange plate slenderness ratio (b/t) on column strength
Figure 6 shows effects of flange plate slenderness ratio on the column strength curve of
PEC columns. Three different flange plate slenderness ratios (b/t =25, b/t = 30, b/t = 35)
are selected to observe the influence of this parameter on the failure envelope of slender
PEC column. From the Fig. 6, it is obvious that a significant reduction in failure
envelope is found with the increase of the flange plate slenderness ratio of slender PEC
Ax
ial
Lo
ad
(kN
)
Moment (kN-
m)
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 263
column. An average reduction in strength of 15% is noted in compression zone, when
the flange plate slenderness ratio is varied from 25 to 30 whereas in weak axis bending
2% extra drop in strength is noticed. Moreover, by changing the flange plate slenderness
ratio from 30 to 35, average drop in strength is observed as nearly 15% and 16% for
strong and weak axis bending respectively. Besides, brittle behaviour of slender PEC
column is pronounced with the increase of flange plate slenderness ratio.
(a) Strong axis bending
(b) Weak axis bending
Figure 6: Effect of flange plate slenderness ratio (b/t) on interaction diagram of slender PEC
column (a) Strong axis (b) Weak axis
264 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
3.3 Effect of Concrete Strength (F’c) on Column Strength Curve
The effects of concrete strength on the load-moment interaction diagram of PEC
columns are illustrated in Fig. 7.
Figure 7: Effect of concrete strength on interaction diagram of slender PEC columns (a) Strong
axis (b) Weak axis
Malaysian Journal of Civil Engineering 25(2):254-266(2013) 265
Normal strength concrete of f'c = 30 MPa and high strength of concrete f'c = 60 MPa are
selected (which are normally used in our country) to observe the overall effect of this
parameter on the failure envelope of slender PEC column. The increase in the zone of
failure envelope between the two load moment interaction diagrams is found quite
significant with the increase of the concrete strength to such large extent. Additionally, a
greater increase in strength is found in compression zone compared to that of the tension
zone of the interaction diagrams for the increment of 30 MPa in the strength of concrete.
An average increase of 40% is noted in compression zone in strong axis bending
whereas in weak axis bending it becomes 33% when the concrete strength is varied from
30 MPa to 60 MPa. However, when bending under weak axis is considered, use of high
strength concrete can produce brittle concrete. In such cases, high performance (fibre
reinforced) concrete can be used to increase ductility of slender PEC column.
4.0 Conclusions and Suggestions for Future Work
The numerical procedure implemented in this study is limited to the following
assumptions,
i) Strains between concrete and structural steel are compatible and no slip
occurred.
ii) The strain is linearly proportional to the distance from the neutral axis.
iii) The confinement of the concrete provided by transverse links and the
structural steel section is not considered.
iv) The effects of residual stresses on steel section are neglected.
v) The strain hardening of steel is not included.
To observe the strength and ductility of slender PEC column through column strength
curve, Newmark’s numerical iterative procedure is used. Several parameters like overall
column slenderness ratio, flange plate slenderness ratio and concrete strength are varied
to observe the influence of these parameters on column strength curve of slender PEC
column. Decrease in strength is found with the increase of overall column slenderness
ratio and flange plate slenderness ratio. When the slenderness ratio reaches to 25, the
reduction in strength is more significant. Second order moment in column which
increases due to the increase of slenderness ratio, is the main reason of lowering the
strength of slender PEC column. At the same time, ductility is also reduced with the
increase of these variables. As the strength of concrete increases, strength of slender
PEC column increases in large amount. It happens due to the increase of stiffness of
PEC column with the increase of concrete stiffness. Similar trend in reduction of
strength of ductility is found for both strong and weak axis bending. However, the
reduction rate is more significant in weak axis bending as lower stiffness is attained
here.
266 Malaysian Journal of Civil Engineering 25(2):254-266(2013)
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